Properties

Label 151.1.b.a.150.1
Level $151$
Weight $1$
Character 151.150
Self dual yes
Analytic conductor $0.075$
Analytic rank $0$
Dimension $3$
Projective image $D_{7}$
CM discriminant -151
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 151 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 151.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.0753588169076\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
Defining polynomial: \(x^{3} - x^{2} - 2 x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{7}\)
Projective field: Galois closure of 7.1.3442951.1
Artin image: $D_7$
Artin field: Galois closure of 7.1.3442951.1

Embedding invariants

Embedding label 150.1
Root \(1.80194\) of defining polynomial
Character \(\chi\) \(=\) 151.150

$q$-expansion

\(f(q)\) \(=\) \(q-1.80194 q^{2} +2.24698 q^{4} -0.445042 q^{5} -2.24698 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.80194 q^{2} +2.24698 q^{4} -0.445042 q^{5} -2.24698 q^{8} +1.00000 q^{9} +0.801938 q^{10} +1.24698 q^{11} +1.80194 q^{16} +1.24698 q^{17} -1.80194 q^{18} -1.80194 q^{19} -1.00000 q^{20} -2.24698 q^{22} -0.801938 q^{25} -1.80194 q^{29} -0.445042 q^{31} -1.00000 q^{32} -2.24698 q^{34} +2.24698 q^{36} +1.24698 q^{37} +3.24698 q^{38} +1.00000 q^{40} -0.445042 q^{43} +2.80194 q^{44} -0.445042 q^{45} -1.80194 q^{47} +1.00000 q^{49} +1.44504 q^{50} -0.554958 q^{55} +3.24698 q^{58} -0.445042 q^{59} +0.801938 q^{62} +2.80194 q^{68} -2.24698 q^{72} -2.24698 q^{74} -4.04892 q^{76} -0.801938 q^{80} +1.00000 q^{81} -0.554958 q^{85} +0.801938 q^{86} -2.80194 q^{88} +0.801938 q^{90} +3.24698 q^{94} +0.801938 q^{95} -1.80194 q^{97} -1.80194 q^{98} +1.24698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - q^{2} + 2q^{4} - q^{5} - 2q^{8} + 3q^{9} + O(q^{10}) \) \( 3q - q^{2} + 2q^{4} - q^{5} - 2q^{8} + 3q^{9} - 2q^{10} - q^{11} + q^{16} - q^{17} - q^{18} - q^{19} - 3q^{20} - 2q^{22} + 2q^{25} - q^{29} - q^{31} - 3q^{32} - 2q^{34} + 2q^{36} - q^{37} + 5q^{38} + 3q^{40} - q^{43} + 4q^{44} - q^{45} - q^{47} + 3q^{49} + 4q^{50} - 2q^{55} + 5q^{58} - q^{59} - 2q^{62} + 4q^{68} - 2q^{72} - 2q^{74} - 3q^{76} + 2q^{80} + 3q^{81} - 2q^{85} - 2q^{86} - 4q^{88} - 2q^{90} + 5q^{94} - 2q^{95} - q^{97} - q^{98} - q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/151\mathbb{Z}\right)^\times\).

\(n\) \(6\)
\(\chi(n)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) 2.24698 2.24698
\(5\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) −2.24698 −2.24698
\(9\) 1.00000 1.00000
\(10\) 0.801938 0.801938
\(11\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.80194 1.80194
\(17\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(18\) −1.80194 −1.80194
\(19\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(20\) −1.00000 −1.00000
\(21\) 0 0
\(22\) −2.24698 −2.24698
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) −0.801938 −0.801938
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(30\) 0 0
\(31\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(32\) −1.00000 −1.00000
\(33\) 0 0
\(34\) −2.24698 −2.24698
\(35\) 0 0
\(36\) 2.24698 2.24698
\(37\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(38\) 3.24698 3.24698
\(39\) 0 0
\(40\) 1.00000 1.00000
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(44\) 2.80194 2.80194
\(45\) −0.445042 −0.445042
\(46\) 0 0
\(47\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(48\) 0 0
\(49\) 1.00000 1.00000
\(50\) 1.44504 1.44504
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) −0.554958 −0.554958
\(56\) 0 0
\(57\) 0 0
\(58\) 3.24698 3.24698
\(59\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0.801938 0.801938
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 2.80194 2.80194
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −2.24698 −2.24698
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) −2.24698 −2.24698
\(75\) 0 0
\(76\) −4.04892 −4.04892
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −0.801938 −0.801938
\(81\) 1.00000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) −0.554958 −0.554958
\(86\) 0.801938 0.801938
\(87\) 0 0
\(88\) −2.80194 −2.80194
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0.801938 0.801938
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 3.24698 3.24698
\(95\) 0.801938 0.801938
\(96\) 0 0
\(97\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(98\) −1.80194 −1.80194
\(99\) 1.24698 1.24698
\(100\) −1.80194 −1.80194
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 1.00000 1.00000
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −4.04892 −4.04892
\(117\) 0 0
\(118\) 0.801938 0.801938
\(119\) 0 0
\(120\) 0 0
\(121\) 0.554958 0.554958
\(122\) 0 0
\(123\) 0 0
\(124\) −1.00000 −1.00000
\(125\) 0.801938 0.801938
\(126\) 0 0
\(127\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(128\) 1.00000 1.00000
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −2.80194 −2.80194
\(137\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(138\) 0 0
\(139\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.80194 1.80194
\(145\) 0.801938 0.801938
\(146\) 0 0
\(147\) 0 0
\(148\) 2.80194 2.80194
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 1.00000 1.00000
\(152\) 4.04892 4.04892
\(153\) 1.24698 1.24698
\(154\) 0 0
\(155\) 0.198062 0.198062
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.445042 0.445042
\(161\) 0 0
\(162\) −1.80194 −1.80194
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) 1.00000 1.00000
\(171\) −1.80194 −1.80194
\(172\) −1.00000 −1.00000
\(173\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.24698 2.24698
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) −1.00000 −1.00000
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.554958 −0.554958
\(186\) 0 0
\(187\) 1.55496 1.55496
\(188\) −4.04892 −4.04892
\(189\) 0 0
\(190\) −1.44504 −1.44504
\(191\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(192\) 0 0
\(193\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(194\) 3.24698 3.24698
\(195\) 0 0
\(196\) 2.24698 2.24698
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −2.24698 −2.24698
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 1.80194 1.80194
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −2.24698 −2.24698
\(207\) 0 0
\(208\) 0 0
\(209\) −2.24698 −2.24698
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.198062 0.198062
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −1.24698 −1.24698
\(221\) 0 0
\(222\) 0 0
\(223\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(224\) 0 0
\(225\) −0.801938 −0.801938
\(226\) 0 0
\(227\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(228\) 0 0
\(229\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.04892 4.04892
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0.801938 0.801938
\(236\) −1.00000 −1.00000
\(237\) 0 0
\(238\) 0 0
\(239\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(240\) 0 0
\(241\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(242\) −1.00000 −1.00000
\(243\) 0 0
\(244\) 0 0
\(245\) −0.445042 −0.445042
\(246\) 0 0
\(247\) 0 0
\(248\) 1.00000 1.00000
\(249\) 0 0
\(250\) −1.44504 −1.44504
\(251\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0.801938 0.801938
\(255\) 0 0
\(256\) −1.80194 −1.80194
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −1.80194 −1.80194
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 2.24698 2.24698
\(273\) 0 0
\(274\) 0.801938 0.801938
\(275\) −1.00000 −1.00000
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 3.24698 3.24698
\(279\) −0.445042 −0.445042
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −1.00000
\(289\) 0.554958 0.554958
\(290\) −1.44504 −1.44504
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0.198062 0.198062
\(296\) −2.80194 −2.80194
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) −1.80194 −1.80194
\(303\) 0 0
\(304\) −3.24698 −3.24698
\(305\) 0 0
\(306\) −2.24698 −2.24698
\(307\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.356896 −0.356896
\(311\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(312\) 0 0
\(313\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) −2.24698 −2.24698
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.24698 −2.24698
\(324\) 2.24698 2.24698
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(332\) 0 0
\(333\) 1.24698 1.24698
\(334\) −3.60388 −3.60388
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) −1.80194 −1.80194
\(339\) 0 0
\(340\) −1.24698 −1.24698
\(341\) −0.554958 −0.554958
\(342\) 3.24698 3.24698
\(343\) 0 0
\(344\) 1.00000 1.00000
\(345\) 0 0
\(346\) 3.24698 3.24698
\(347\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(348\) 0 0
\(349\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.24698 −1.24698
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 1.00000 1.00000
\(361\) 2.24698 2.24698
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 1.00000 1.00000
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −2.80194 −2.80194
\(375\) 0 0
\(376\) 4.04892 4.04892
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 1.80194 1.80194
\(381\) 0 0
\(382\) 3.24698 3.24698
\(383\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0.801938 0.801938
\(387\) −0.445042 −0.445042
\(388\) −4.04892 −4.04892
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −2.24698 −2.24698
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 2.80194 2.80194
\(397\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −1.44504 −1.44504
\(401\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −0.445042 −0.445042
\(406\) 0 0
\(407\) 1.55496 1.55496
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 2.80194 2.80194
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 4.04892 4.04892
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) −1.80194 −1.80194
\(424\) 0 0
\(425\) −1.00000 −1.00000
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) −0.356896 −0.356896
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(440\) 1.24698 1.24698
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −2.24698 −2.24698
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 1.44504 1.44504
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −2.24698 −2.24698
\(455\) 0 0
\(456\) 0 0
\(457\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(458\) 3.24698 3.24698
\(459\) 0 0
\(460\) 0 0
\(461\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(462\) 0 0
\(463\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(464\) −3.24698 −3.24698
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −1.44504 −1.44504
\(471\) 0 0
\(472\) 1.00000 1.00000
\(473\) −0.554958 −0.554958
\(474\) 0 0
\(475\) 1.44504 1.44504
\(476\) 0 0
\(477\) 0 0
\(478\) −2.24698 −2.24698
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −2.24698 −2.24698
\(483\) 0 0
\(484\) 1.24698 1.24698
\(485\) 0.801938 0.801938
\(486\) 0 0
\(487\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0.801938 0.801938
\(491\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(492\) 0 0
\(493\) −2.24698 −2.24698
\(494\) 0 0
\(495\) −0.554958 −0.554958
\(496\) −0.801938 −0.801938
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 1.80194 1.80194
\(501\) 0 0
\(502\) −3.60388 −3.60388
\(503\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) −1.00000 −1.00000
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 2.24698 2.24698
\(513\) 0 0
\(514\) 0 0
\(515\) −0.554958 −0.554958
\(516\) 0 0
\(517\) −2.24698 −2.24698
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(522\) 3.24698 3.24698
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −0.554958 −0.554958
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) −0.445042 −0.445042
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −2.24698 −2.24698
\(539\) 1.24698 1.24698
\(540\) 0 0
\(541\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.24698 −1.24698
\(545\) 0 0
\(546\) 0 0
\(547\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(548\) −1.00000 −1.00000
\(549\) 0 0
\(550\) 1.80194 1.80194
\(551\) 3.24698 3.24698
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −4.04892 −4.04892
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0.801938 0.801938
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(570\) 0 0
\(571\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(578\) −1.00000 −1.00000
\(579\) 0 0
\(580\) 1.80194 1.80194
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 0.801938 0.801938
\(590\) −0.356896 −0.356896
\(591\) 0 0
\(592\) 2.24698 2.24698
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 2.24698 2.24698
\(605\) −0.246980 −0.246980
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 1.80194 1.80194
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 2.80194 2.80194
\(613\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(614\) −2.24698 −2.24698
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0.445042 0.445042
\(621\) 0 0
\(622\) 0.801938 0.801938
\(623\) 0 0
\(624\) 0 0
\(625\) 0.445042 0.445042
\(626\) 0.801938 0.801938
\(627\) 0 0
\(628\) 0 0
\(629\) 1.55496 1.55496
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.198062 0.198062
\(636\) 0 0
\(637\) 0 0
\(638\) 4.04892 4.04892
\(639\) 0 0
\(640\) −0.445042 −0.445042
\(641\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(642\) 0 0
\(643\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 4.04892 4.04892
\(647\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(648\) −2.24698 −2.24698
\(649\) −0.554958 −0.554958
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) −2.24698 −2.24698
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −2.24698 −2.24698
\(667\) 0 0
\(668\) 4.49396 4.49396
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 2.24698 2.24698
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 1.24698 1.24698
\(681\) 0 0
\(682\) 1.00000 1.00000
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −4.04892 −4.04892
\(685\) 0.198062 0.198062
\(686\) 0 0
\(687\) 0 0
\(688\) −0.801938 −0.801938
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) −4.04892 −4.04892
\(693\) 0 0
\(694\) −3.60388 −3.60388
\(695\) 0.801938 0.801938
\(696\) 0 0
\(697\) 0 0
\(698\) −2.24698 −2.24698
\(699\) 0 0
\(700\) 0 0
\(701\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(702\) 0 0
\(703\) −2.24698 −2.24698
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) −0.801938 −0.801938
\(721\) 0 0
\(722\) −4.04892 −4.04892
\(723\) 0 0
\(724\) 0 0
\(725\) 1.44504 1.44504
\(726\) 0 0
\(727\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) −0.554958 −0.554958
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) −1.24698 −1.24698
\(741\) 0 0
\(742\) 0 0
\(743\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 3.49396 3.49396
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) −3.24698 −3.24698
\(753\) 0 0
\(754\) 0 0
\(755\) −0.445042 −0.445042
\(756\) 0 0
\(757\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −1.80194 −1.80194
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −4.04892 −4.04892
\(765\) −0.554958 −0.554958
\(766\) 0.801938 0.801938
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.00000 −1.00000
\(773\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(774\) 0.801938 0.801938
\(775\) 0.356896 0.356896
\(776\) 4.04892 4.04892
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.80194 1.80194
\(785\) 0 0
\(786\) 0 0
\(787\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −2.80194 −2.80194
\(793\) 0 0
\(794\) 3.24698 3.24698
\(795\) 0 0
\(796\) 0 0
\(797\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(798\) 0 0
\(799\) −2.24698 −2.24698
\(800\) 0.801938 0.801938
\(801\) 0 0
\(802\) 3.24698 3.24698
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0.801938 0.801938
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −2.80194 −2.80194
\(815\) 0 0
\(816\) 0 0
\(817\) 0.801938 0.801938
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(824\) −2.80194 −2.80194
\(825\) 0 0
\(826\) 0 0
\(827\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(828\) 0 0
\(829\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1.24698 1.24698
\(834\) 0 0
\(835\) −0.890084 −0.890084
\(836\) −5.04892 −5.04892
\(837\) 0 0
\(838\) 0 0
\(839\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(840\) 0 0
\(841\) 2.24698 2.24698
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −0.445042 −0.445042
\(846\) 3.24698 3.24698
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 1.80194 1.80194
\(851\) 0 0
\(852\) 0 0
\(853\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(854\) 0 0
\(855\) 0.801938 0.801938
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0.445042 0.445042
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0.801938 0.801938
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −1.80194 −1.80194
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) −2.24698 −2.24698
\(879\) 0 0
\(880\) −1.00000 −1.00000
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −1.80194 −1.80194
\(883\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 1.24698 1.24698
\(892\) 2.80194 2.80194
\(893\) 3.24698 3.24698
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0.801938 0.801938
\(900\) −1.80194 −1.80194
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(908\) 2.80194 2.80194
\(909\) 0 0
\(910\) 0 0
\(911\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.801938 0.801938
\(915\) 0 0
\(916\) −4.04892 −4.04892
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −2.24698 −2.24698
\(923\) 0 0
\(924\) 0 0
\(925\) −1.00000 −1.00000
\(926\) −2.24698 −2.24698
\(927\) 1.24698 1.24698
\(928\) 1.80194 1.80194
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) −1.80194 −1.80194
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −0.692021 −0.692021
\(936\) 0 0
\(937\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 1.80194 1.80194
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −0.801938 −0.801938
\(945\) 0 0
\(946\) 1.00000 1.00000
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −2.60388 −2.60388
\(951\) 0 0
\(952\) 0 0
\(953\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(954\) 0 0
\(955\) 0.801938 0.801938
\(956\) 2.80194 2.80194
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −0.801938 −0.801938
\(962\) 0 0
\(963\) 0 0
\(964\) 2.80194 2.80194
\(965\) 0.198062 0.198062
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −1.24698 −1.24698
\(969\) 0 0
\(970\) −1.44504 −1.44504
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 3.24698 3.24698
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −1.00000 −1.00000
\(981\) 0 0
\(982\) 0.801938 0.801938
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 4.04892 4.04892
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 1.00000 1.00000
\(991\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(992\) 0.445042 0.445042
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 151.1.b.a.150.1 3
3.2 odd 2 1359.1.d.b.1207.3 3
4.3 odd 2 2416.1.e.a.2113.2 3
5.2 odd 4 3775.1.c.c.3774.1 6
5.3 odd 4 3775.1.c.c.3774.6 6
5.4 even 2 3775.1.d.d.301.3 3
151.150 odd 2 CM 151.1.b.a.150.1 3
453.452 even 2 1359.1.d.b.1207.3 3
604.603 even 2 2416.1.e.a.2113.2 3
755.452 even 4 3775.1.c.c.3774.1 6
755.603 even 4 3775.1.c.c.3774.6 6
755.754 odd 2 3775.1.d.d.301.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
151.1.b.a.150.1 3 1.1 even 1 trivial
151.1.b.a.150.1 3 151.150 odd 2 CM
1359.1.d.b.1207.3 3 3.2 odd 2
1359.1.d.b.1207.3 3 453.452 even 2
2416.1.e.a.2113.2 3 4.3 odd 2
2416.1.e.a.2113.2 3 604.603 even 2
3775.1.c.c.3774.1 6 5.2 odd 4
3775.1.c.c.3774.1 6 755.452 even 4
3775.1.c.c.3774.6 6 5.3 odd 4
3775.1.c.c.3774.6 6 755.603 even 4
3775.1.d.d.301.3 3 5.4 even 2
3775.1.d.d.301.3 3 755.754 odd 2